ACTIVITY: Classifying Polynomials Using Algebra Tiles

Size: px
Start display at page:

Download "ACTIVITY: Classifying Polynomials Using Algebra Tiles"

Transcription

1 7. Polynomials classify polynomials? How can you use algebra tiles to model and ACTIVITY: Meaning of Prefixes Work with a partner. Think of a word that uses one of the prefixes with one of the base words. Then define the word and write a sentence that uses the word. Prefix Mono Bi Tri Poly Base Word Dactyl Cycle Ped Syllabic 2 ACTIVITY: Classifying Polynomials Using Algebra Tiles Work with a partner. Six different algebra tiles are shown at the right. x x x 2 x 2 Write the polynomial that is modeled by the algebra tiles. Then classify the polynomial as a monomial, binomial, or trinomial. Explain your reasoning. COMMON CORE Polynomials In this lesson, you will find the degrees of monomials. classify polynomials. Applying Standard A.SSE.a a. b. c. d. e. f. 28 Chapter 7 Polynomial Equations and Factoring

2 ACTIVITY: Solving an Algebra Tile Puzzle Math Practice Use Expressions What do the shapes and colors of the tiles represent? How does this help you write a polynomial? Work with a partner. Write the polynomial modeled by the algebra tiles, evaluate the polynomial at the given value, and write the result in the corresponding square of the Sudoku puzzle. Then solve the puzzle. A, H7 Value when x = 2 A4, B, E5, G6, I7 Value when x = 2 A B C D E F G H I A6, D7, E2, H5 Value when x = B5, F, H Value when x = A7, F9, I4 Value when x = E8, F, I6 Value when x = C4, I Value when x = B7, D Value when x = 2 4. IN YOUR OWN WORDS How can you use algebra tiles to model and classify polynomials? Explain why algebra tiles have the dimensions, shapes, and colors that they have. Use what you learned about modeling polynomials to complete Exercises 5 and 6 on page 2. Section 7. Polynomials 29

3 7. Lesson Lesson Tutorials Key Vocabulary monomial, p. 0 degree of a monomial, p. 0 polynomial, p. binomial, p. trinomial, p. degree of a polynomial, p. A monomial is a number, a variable, or a product of a number and one or more variables with whole number exponents. Monomials 4 2 y 2 2.5x 2 y Not monomials x.5 2 z Reason Monomials must have whole number exponents. Monomials cannot have variables in the denominator. 7 y Monomials cannot have variable exponents. The degree of a monomial is the sum of the exponents of the variables in the monomial. EXAMPLE Finding the Degrees of Monomials Find the degree of each monomial. a. 5x 2 The exponent of x is 2. So, the degree of the monomial is 2. Remember For any nonzero number a, a 0 =. b. 2 xy c. The exponent of x is and the exponent of y is. The sum of the exponents is + = 4. So, the degree of the monomial is 4. You can rewrite as x 0. The exponent of x is 0. So, the degree of the monomial is 0. Exercises 7 4 Find the degree of the monomial.. x c d 2. 5 y Chapter 7 Polynomial Equations and Factoring

4 A polynomial is a monomial or a sum of monomials. Each monomial is called a term of the polynomial. A polynomial with two terms is a binomial. A polynomial with three terms is a trinomial. 5x + 2 x 2 + 5x + 2 The degree of a polynomial is the greatest degree of its terms. A polynomial in one variable is in standard form when the exponents of the terms decrease from left to right. EXAMPLE 2 Classifying Polynomials Write each polynomial in standard form. Identify the degree and classify each polynomial by the number of terms. Polynomial Standard Form Degree Type of Polynomial a. z 4 z 4 4 monomial b x 2 x 5x 2 x trinomial c. 8q + q 5 q 5 + 8q 5 binomial EXAMPLE v 0 0 ft/sec Real-Life Application The polynomial 6t 2 + v 0 t + s 0 represents the height (in feet) of an object, where v 0 is the initial vertical velocity (in feet per second), s 0 is the initial height of the object (in feet), and t is the time (in seconds). a. Write a polynomial that represents the height of the baseball. 6t 2 + v 0 t + s 0 = 6t 2 + 0t + 4 Substitute 0 for v 0 and 4 for s 0. b. What is the height of the baseball after second? 6t 2 + 0t + 4 = 6() 2 + 0() + 4 Substitute for t. s 0 4 ft = Simplify. = 8 Add. The height of the baseball after second is 8 feet. Exercises 5 2 Write the polynomial in standard form. Identify the degree and classify the polynomial by the number of terms z 6. t 2 t 0t x + x 8. In Example, the initial height is 5 feet. What is the height of the baseball after 2 seconds? Section 7. Polynomials

5 Exercises 7. Help with Homework π. WRITING Is a monomial? Explain your reasoning. 2. VOCABULARY When is a polynomial in one variable in standard form?. OPEN-ENDED Write a trinomial of degree 5 in standard form. 4. WHICH ONE DOESN T BELONG? Which expression does not belong with the other three? Explain your reasoning. a + 4a b 2 8x 6y 8z 6)= 9+(- )= +(- 9)= 4+(- = ) 9+(- Use algebra tiles to represent the polynomial. 5. x 2 + 2x x 2 x + Find the degree of the monomial. 7. 4g..75k x 4 9. s8t 8. 2π 2. m2n q 4rs 6 Write the polynomial in standard form. Identify the degree and classify the polynomial by the number of terms p w d 2 4d c 2 +.2c 4 c 9. 4v v y y z n n 24. ERROR ANALYSIS Describe and correct the error in writing the polynomial in standard form πr 2 r 8 + 2r 5 polynomial: m 2 5m5 + m4 standard form: 5m5 + m2 + m SPHERE The expression πr represents the volume of a sphere with radius r. Why is this expression a monomial? What is its degree? 2 Chapter 7 Polynomial Equations and Factoring

6 Tell whether the expression is a polynomial. If so, identify the degree and classify the polynomial by the number of terms. 26. g x 2x y k 5 + 4k k 0. LOGIC The polynomial d 2 πr 2 represents the area of a region, where d is the diameter of a circle and r is the radius of the circle. How can this happen? Justify your answer with a diagram. Use the polynomial 6t 2 + v0t + s0 to write a polynomial that represents the height of the object. Then find the height of the object after second.. WATER BALLOON You throw a water balloon from a building. 2. TENNIS You bounce a tennis ball on a racket. v0 â Ź45 ft/sec v0 â 6 ft/sec s0 â 200 ft s0 â ft Not drawn to scale. The polynomial w w represents the area of a rectangular garden with a width of w feet. a. Use guess, check, and revise to find the width of the garden with the maximum area. (Hint: The width is between 0 feet and 8 feet.) b. What is the perimeter of the garden? 7 c. How many seed packets do you need for the garden? 7 Simplify the expression. (Skills Review Handbook) 4. 2x + 4y + x x x + 5y 7y x x + x 7. MULTIPLE CHOICE What is the surface area of the prism? (Skills Review Handbook) A x ft B (24x + 6) ft C (6x + 24) ft D (60x + 2) ft ft 2 ft 6x ft Section 7. Polynomials

Fair Game Review. Chapter 7. Simplify the expression. Write an expression for the perimeter of the figure

Fair Game Review. Chapter 7. Simplify the expression. Write an expression for the perimeter of the figure Name Date Chapter 7 Simplify the expression. Fair Game Review 1. 5y + 6 9y. h + 11 + 3h 4 + + 4. 7 ( m + 8) 3. 8a 10 4a 6 a 5. 5 ( d + 3) + 4( d 6) 6. q ( q ) 16 + 9 + 7 Write an expression for the perimeter

More information

ACTIVITY: Factoring Special Products. Work with a partner. Six different algebra tiles are shown below.

ACTIVITY: Factoring Special Products. Work with a partner. Six different algebra tiles are shown below. 7.9 Factoring Special Products special products? How can you recognize and factor 1 ACTIVITY: Factoring Special Products Work with a partner. Six different algebra tiles are shown below. 1 1 x x x 2 x

More information

Adding and Subtracting Polynomials

Adding and Subtracting Polynomials 7.2 Adding and Subtracting Polynomials subtract polynomials? How can you add polynomials? How can you 1 EXAMPLE: Adding Polynomials Using Algebra Tiles Work with a partner. Six different algebra tiles

More information

SEE the Big Idea. of a Falling Object (p. 400) Game Reserve (p. 394) Photo Cropping (p. 390) Gateway Arch (p. 382) Framing a Photo (p.

SEE the Big Idea. of a Falling Object (p. 400) Game Reserve (p. 394) Photo Cropping (p. 390) Gateway Arch (p. 382) Framing a Photo (p. 7 Polynomial Equations and Factoring 7.1 Adding and Subtracting Polynomials 7.2 Multiplying Polynomials 7.3 Special Products of Polynomials 7.4 Solving Polynomial Equations in Factored Form 7.5 Factoring

More information

Adding and Subtracting Polynomials Polynomials in the Sun

Adding and Subtracting Polynomials Polynomials in the Sun Adding and Subtracting Polynomials SUGGESTED LEARNING STRATEGIES: Shared Reading, Questioning the Text, Create Representations, Vocabulary Organizer, Note Taking A solar panel is a device that collects

More information

7.7. Factoring Special Products. Essential Question How can you recognize and factor special products?

7.7. Factoring Special Products. Essential Question How can you recognize and factor special products? 7.7 Factoring Special Products Essential Question How can you recognize and factor special products? Factoring Special Products LOOKING FOR STRUCTURE To be proficient in math, you need to see complicated

More information

Maintaining Mathematical Proficiency

Maintaining Mathematical Proficiency Chapter 7 Maintaining Mathematical Proficiency Simplify the expression. 1. 5x 6 + 3x. 3t + 7 3t 4 3. 8s 4 + 4s 6 5s 4. 9m + 3 + m 3 + 5m 5. 4 3p 7 3p 4 1 z 1 + 4 6. ( ) 7. 6( x + ) 4 8. 3( h + 4) 3( h

More information

Factoring Polynomials Using the GCF

Factoring Polynomials Using the GCF 7.6 Factoring Polynomials Using the GCF polynomial in factored form? How can you use common factors to write a 1 ACTIVITY: Finding Monomial Factors Work with a partner. Six different algebra tiles are

More information

Unit 5 AB Quadratic Expressions and Equations 1/9/2017 2/8/2017

Unit 5 AB Quadratic Expressions and Equations 1/9/2017 2/8/2017 Unit 5 AB Quadratic Expressions and Equations 1/9/2017 2/8/2017 Name: By the end of this unit, you will be able to Add, subtract, and multiply polynomials Solve equations involving the products of monomials

More information

Ready To Go On? Skills Intervention 7-1 Integer Exponents

Ready To Go On? Skills Intervention 7-1 Integer Exponents 7A Evaluating Expressions with Zero and Negative Exponents Zero Exponent: Any nonzero number raised to the zero power is. 4 0 Ready To Go On? Skills Intervention 7-1 Integer Exponents Negative Exponent:

More information

Review for Mastery. Integer Exponents. Zero Exponents Negative Exponents Negative Exponents in the Denominator. Definition.

Review for Mastery. Integer Exponents. Zero Exponents Negative Exponents Negative Exponents in the Denominator. Definition. LESSON 6- Review for Mastery Integer Exponents Remember that means 8. The base is, the exponent is positive. Exponents can also be 0 or negative. Zero Exponents Negative Exponents Negative Exponents in

More information

How can you factor the trinomial x 2 + bx + c into the product of two binomials? ACTIVITY: Finding Binomial Factors

How can you factor the trinomial x 2 + bx + c into the product of two binomials? ACTIVITY: Finding Binomial Factors 7.7 Factoring x 2 + bx + c How can you factor the trinomial x 2 + bx + c into the product of two binomials? 1 ACTIVITY: Finding Binomial Factors Work with a partner. Six different algebra tiles are shown

More information

I CAN classify polynomials by degree and by the number of terms.

I CAN classify polynomials by degree and by the number of terms. 13-1 Polynomials I CAN classify polynomials by degree and by the number of terms. 13-1 Polynomials Insert Lesson Title Here Vocabulary monomial polynomial binomial trinomial degree of a polynomial 13-1

More information

Unit 13: Polynomials and Exponents

Unit 13: Polynomials and Exponents Section 13.1: Polynomials Section 13.2: Operations on Polynomials Section 13.3: Properties of Exponents Section 13.4: Multiplication of Polynomials Section 13.5: Applications from Geometry Section 13.6:

More information

A Five Day Exploration of Polynomials Using Algebra Tiles and the TI-83 Plus Graphing Calculator

A Five Day Exploration of Polynomials Using Algebra Tiles and the TI-83 Plus Graphing Calculator Page 1. A Five Day Exploration of Polynomials Using Algebra Tiles and the TI-83 Plus Graphing Calculator Pre- Algebra Grade Seven By: Cory Savard Page. Overall Unit Objectives Upon completion of this unit,

More information

Unit 5 Quadratic Expressions and Equations

Unit 5 Quadratic Expressions and Equations Unit 5 Quadratic Expressions and Equations Test Date: Name: By the end of this unit, you will be able to Add, subtract, and multiply polynomials Solve equations involving the products of monomials and

More information

Controlling the Population

Controlling the Population Lesson.1 Skills Practice Name Date Controlling the Population Adding and Subtracting Polynomials Vocabulary Match each definition with its corresponding term. 1. polynomial a. a polynomial with only 1

More information

Copy anything you do not already have memorized into your notes.

Copy anything you do not already have memorized into your notes. Copy anything you do not already have memorized into your notes. A monomial is the product of non-negative integer powers of variables. ONLY ONE TERM. ( mono- means one) No negative exponents which means

More information

Something that can have different values at different times. A variable is usually represented by a letter in algebraic expressions.

Something that can have different values at different times. A variable is usually represented by a letter in algebraic expressions. Lesson Objectives: Students will be able to define, recognize and use the following terms in the context of polynomials: o Constant o Variable o Monomial o Binomial o Trinomial o Polynomial o Numerical

More information

Looking Ahead to Chapter 10

Looking Ahead to Chapter 10 Looking Ahead to Chapter Focus In Chapter, you will learn about polynomials, including how to add, subtract, multiply, and divide polynomials. You will also learn about polynomial and rational functions.

More information

POLYNOMIAL ADDITION AND MULTIPLICATION

POLYNOMIAL ADDITION AND MULTIPLICATION Topic 23: Polynomial addition and multiplication 377 POLYNOMIAL ADDITION AND MULTIPLICATION Lesson 23.1 Introduction to polynomials 23.1 OPENER The Bradley family has decided to build a house in a new

More information

Quadratic Expressions and Equations

Quadratic Expressions and Equations Unit 5 Quadratic Expressions and Equations 1/9/2017 2/8/2017 Name: By the end of this unit, you will be able to Add, subtract, and multiply polynomials Solve equations involving the products of monomials

More information

Intensive Math-Algebra I Mini-Lesson MA.912.A.4.3

Intensive Math-Algebra I Mini-Lesson MA.912.A.4.3 Intensive Math-Algebra I Mini-Lesson M912.4.3 Summer 2013 Factoring Polynomials Student Packet Day 15 Name: Date: Benchmark M912.4.3 Factor polynomials expressions This benchmark will be assessed using

More information

Quick-and-Easy Factoring. of lower degree; several processes are available to fi nd factors.

Quick-and-Easy Factoring. of lower degree; several processes are available to fi nd factors. Lesson 11-3 Quick-and-Easy Factoring BIG IDEA Some polynomials can be factored into polynomials of lower degree; several processes are available to fi nd factors. Vocabulary factoring a polynomial factored

More information

Polynomials. Title Page. Prior Knowledge: understanding of coefficients and terms

Polynomials. Title Page. Prior Knowledge: understanding of coefficients and terms Polynomials Title Page Subject: Polynomials Topic: Classifying Polynomials by Degree and Number of Terms. Also a review of Coefficients. Grade(s): 8th 10th grade Prior Knowledge: understanding of coefficients

More information

Unit 2-1: Factoring and Solving Quadratics. 0. I can add, subtract and multiply polynomial expressions

Unit 2-1: Factoring and Solving Quadratics. 0. I can add, subtract and multiply polynomial expressions CP Algebra Unit -1: Factoring and Solving Quadratics NOTE PACKET Name: Period Learning Targets: 0. I can add, subtract and multiply polynomial expressions 1. I can factor using GCF.. I can factor by grouping.

More information

The number part of a term with a variable part. Terms that have the same variable parts. Constant terms are also like terms.

The number part of a term with a variable part. Terms that have the same variable parts. Constant terms are also like terms. Algebra Notes Section 9.1: Add and Subtract Polynomials Objective(s): To be able to add and subtract polynomials. Recall: Coefficient (p. 97): Term of a polynomial (p. 97): Like Terms (p. 97): The number

More information

Essential Question How can you factor a polynomial completely?

Essential Question How can you factor a polynomial completely? REASONING ABSTRACTLY 7.8 To be proficient in math, ou need to know and flexibl use different properties of operations and objects. Factoring Polnomials Completel Essential Question How can ou factor a

More information

Lesson 2: Introduction to Variables

Lesson 2: Introduction to Variables Lesson 2: Introduction to Variables Topics and Objectives: Evaluating Algebraic Expressions Some Vocabulary o Variable o Term o Coefficient o Constant o Factor Like Terms o Identifying Like Terms o Combining

More information

Day 131 Practice. What Can You Do With Polynomials?

Day 131 Practice. What Can You Do With Polynomials? Polynomials Monomial - a Number, a Variable or a PRODUCT of a number and a variable. Monomials cannot have radicals with variables inside, quotients of variables or variables with negative exponents. Degree

More information

Chapter 8 Polynomials and Factoring

Chapter 8 Polynomials and Factoring Chapter 8 Polynomials and Factoring 8.1 Add and Subtract Polynomials Monomial A. EX: Degree of a monomial the of all of the of the EX: 4x 2 y Polynomial A or EX: Degree of a polynomial the of its terms

More information

Comparing Linear and Nonlinear Functions 5.5. ACTIVITY: Finding Patterns for Similar Figures. How can you recognize when a pattern

Comparing Linear and Nonlinear Functions 5.5. ACTIVITY: Finding Patterns for Similar Figures. How can you recognize when a pattern 5.5 Comparing Linear and Nonlinear Functions in real life is linear or nonlinear? How can ou recognize when a pattern ACTIVITY: Finding Patterns for Similar Figures Work with a partner. Cop and complete

More information

How can you use inductive reasoning to observe patterns and write general rules involving properties of exponents?

How can you use inductive reasoning to observe patterns and write general rules involving properties of exponents? 0. Product of Powers Property How can you use inductive reasoning to observe patterns and write general rules involving properties of exponents? ACTIVITY: Finding Products of Powers Work with a partner.

More information

Factoring x 2 + bx + c

Factoring x 2 + bx + c 7.5 Factoring x 2 + bx + c Essential Question How can you use algebra tiles to factor the trinomial x 2 + bx + c into the product of two binomials? Finding Binomial Factors Work with a partner. Use algebra

More information

Algebra I Polynomials

Algebra I Polynomials Slide 1 / 217 Slide 2 / 217 Algebra I Polynomials 2014-04-24 www.njctl.org Slide 3 / 217 Table of Contents Definitions of Monomials, Polynomials and Degrees Adding and Subtracting Polynomials Multiplying

More information

6-5 Multiplying Polynomials

6-5 Multiplying Polynomials 6-5 Multiplying Polynomials Warm Up Lesson Presentation Lesson Quiz Algebra 1 Warm Up Evaluate. 1.3 2 3.10 2 Simplify. 9 2.2 4 16 100 4.2 3 2 4 6. (5 3 ) 2 2 7 5. y 5 y 4 5 6 7.(x 2 ) 4 y 9 x 8 8. 4(x

More information

Section 9.1: Add and Subtract Polynomials. The number part of a term with a variable part.

Section 9.1: Add and Subtract Polynomials. The number part of a term with a variable part. Algebra Notes Section 9.1: Add and Subtract Polynomials Objective(s): Recall: Coefficient (p. 97): Term of a polynomial (p. 97): Like Terms (p. 97): The number part of a term with a variable part. The

More information

Polynomials. Why Learn This? 730 Chapter A Introduction to. Polynomials. 14B Polynomial Operations

Polynomials. Why Learn This? 730 Chapter A Introduction to. Polynomials. 14B Polynomial Operations CHAPTER 14 Polynomials 14A Introduction to Polynomials 14-1 Polynomials LAB Model Polynomials 14-2 Simplifying Polynomials Use properties to simplify polynomials. Perform operations with polynomials. 14B

More information

Algebra I. Polynomials.

Algebra I. Polynomials. 1 Algebra I Polynomials 2015 11 02 www.njctl.org 2 Table of Contents Definitions of Monomials, Polynomials and Degrees Adding and Subtracting Polynomials Multiplying a Polynomial by a Monomial Multiplying

More information

= The algebraic expression is 3x 2 x The algebraic expression is x 2 + x. 3. The algebraic expression is x 2 2x.

= The algebraic expression is 3x 2 x The algebraic expression is x 2 + x. 3. The algebraic expression is x 2 2x. Chapter 7 Maintaining Mathematical Proficiency (p. 335) 1. 3x 7 x = 3x x 7 = (3 )x 7 = 5x 7. 4r 6 9r 1 = 4r 9r 6 1 = (4 9)r 6 1 = 5r 5 3. 5t 3 t 4 8t = 5t t 8t 3 4 = ( 5 1 8)t 3 4 = ()t ( 1) = t 1 4. 3(s

More information

Name Period Date. polynomials of the form x ± bx ± c. Use guess and check and logic to factor polynomials of the form 2

Name Period Date. polynomials of the form x ± bx ± c. Use guess and check and logic to factor polynomials of the form 2 Name Period Date POLYNOMIALS Student Packet 3: Factoring Polynomials POLY3 STUDENT PAGES POLY3.1 An Introduction to Factoring Polynomials Understand what it means to factor a polynomial Factor polynomials

More information

Student Instruction Sheet: Unit 1 Lesson 3. Polynomials

Student Instruction Sheet: Unit 1 Lesson 3. Polynomials Student Instruction Sheet: Unit 1 Lesson 3 Suggested time: 150 min Polynomials What s important in this lesson: You will use algebra tiles to learn how to add/subtract polynomials. Problems are provided

More information

Why It s Important. What You ll Learn

Why It s Important. What You ll Learn How could you solve this problem? Denali and Mahala weed the borders on the north and south sides of their rectangular yard. Denali starts first and has weeded m on the south side when Mahala says he should

More information

Monomial. 5 1 x A sum is not a monomial. 2 A monomial cannot have a. x 21. degree. 2x 3 1 x 2 2 5x Rewrite a polynomial

Monomial. 5 1 x A sum is not a monomial. 2 A monomial cannot have a. x 21. degree. 2x 3 1 x 2 2 5x Rewrite a polynomial 9.1 Add and Subtract Polynomials Before You added and subtracted integers. Now You will add and subtract polynomials. Why? So you can model trends in recreation, as in Ex. 37. Key Vocabulary monomial degree

More information

Essential Question How can you use a rational exponent to represent a power involving a radical?

Essential Question How can you use a rational exponent to represent a power involving a radical? 5.1 nth Roots and Rational Exponents Essential Question How can you use a rational exponent to represent a power involving a radical? Previously, you learned that the nth root of a can be represented as

More information

Polynomials 370 UNIT 10 WORKING WITH POLYNOMIALS. The railcars are linked together.

Polynomials 370 UNIT 10 WORKING WITH POLYNOMIALS. The railcars are linked together. UNIT 10 Working with Polynomials The railcars are linked together. 370 UNIT 10 WORKING WITH POLYNOMIALS Just as a train is built from linking railcars together, a polynomial is built by bringing terms

More information

Lesson 10.1 Polynomials

Lesson 10.1 Polynomials Lesson 10.1 Polynomials Objectives Classify polynomials. Use algebra tiles to add polynomials. Add and subtract polynomials. A contractor is buying paint to cover the interior of two cubical storage tanks.

More information

MathB65 Ch 4 IV, V, VI.notebook. October 31, 2017

MathB65 Ch 4 IV, V, VI.notebook. October 31, 2017 Part 4: Polynomials I. Exponents & Their Properties II. Negative Exponents III. Scientific Notation IV. Polynomials V. Addition & Subtraction of Polynomials VI. Multiplication of Polynomials VII. Greatest

More information

ACTIVITY: Finding Quotients of Powers. Quotient Repeated Multiplication Form Power

ACTIVITY: Finding Quotients of Powers. Quotient Repeated Multiplication Form Power 10. the same base? How can you divide two powers that have 1 ACTIVITY: Finding Quotients of Powers Work with a partner. a. Copy and complete the table. Quotient Repeated Multiplication Form Power 4 ( 4)

More information

Adding and Subtracting Polynomials

Adding and Subtracting Polynomials Exploratory Exercise Kim was working on a problem in math when she ran across this problem. Distribute and simplify if possible. 2(3x + 5) Kim s dad said, I remember doing something like this in school.

More information

For Your Notebook E XAMPLE 1. Factor when b and c are positive KEY CONCEPT. CHECK (x 1 9)(x 1 2) 5 x 2 1 2x 1 9x Factoring x 2 1 bx 1 c

For Your Notebook E XAMPLE 1. Factor when b and c are positive KEY CONCEPT. CHECK (x 1 9)(x 1 2) 5 x 2 1 2x 1 9x Factoring x 2 1 bx 1 c 9.5 Factor x2 1 bx 1 c Before You factored out the greatest common monomial factor. Now You will factor trinomials of the form x 2 1 bx 1 c. Why So you can find the dimensions of figures, as in Ex. 61.

More information

Summer Prep Packet for students entering Algebra 2

Summer Prep Packet for students entering Algebra 2 Summer Prep Packet for students entering Algebra The following skills and concepts included in this packet are vital for your success in Algebra. The Mt. Hebron Math Department encourages all students

More information

How can you use algebra tiles to solve addition or subtraction equations?

How can you use algebra tiles to solve addition or subtraction equations? . Solving Equations Using Addition or Subtraction How can you use algebra tiles to solve addition or subtraction equations? ACTIVITY: Solving Equations Work with a partner. Use algebra tiles to model and

More information

Algebra III and Trigonometry Summer Assignment

Algebra III and Trigonometry Summer Assignment Algebra III and Trigonometry Summer Assignment Welcome to Algebra III and Trigonometry! This summer assignment is a review of the skills you learned in Algebra II. Please bring this assignment with you

More information

Using Properties of Exponents

Using Properties of Exponents 6.1 Using Properties of Exponents Goals p Use properties of exponents to evaluate and simplify expressions involving powers. p Use exponents and scientific notation to solve real-life problems. VOCABULARY

More information

What is a constant? A Constant is a number representing a quantity or value that does not change.

What is a constant? A Constant is a number representing a quantity or value that does not change. Worksheet -: Algebraic Expressions What is a constant? A Constant is a number representing a quantity or value that does not change. What is a variable? A variable is a letter or symbol representing a

More information

ACTIVITY: Simplifying Algebraic Expressions

ACTIVITY: Simplifying Algebraic Expressions . Algebraic Expressions How can you simplify an algebraic expression? ACTIVITY: Simplifying Algebraic Expressions Work with a partner. a. Evaluate each algebraic expression when x = 0 and when x =. Use

More information

Chapter 8 Class Notes 8-A1 (Lessons 8-1&8-2) Monomials and Factoring p Prime Factorization: a whole number expressed as the of factors.

Chapter 8 Class Notes 8-A1 (Lessons 8-1&8-2) Monomials and Factoring p Prime Factorization: a whole number expressed as the of factors. Chapter 8 Class Notes Alg. 1H 8-A1 (Lessons 8-1&8-) Monomials and Factoring p. 40-4 Prime Factorization: a whole number epressed as the of factors. Tree Method: Ladder Method: Factored Form of a Monomial:

More information

Polynomial comes from poly- (meaning "many") and -nomial (in this case meaning "term")... so it says "many terms

Polynomial comes from poly- (meaning many) and -nomial (in this case meaning term)... so it says many terms Polynomials Polynomial comes from poly- (meaning "many") and -nomial (in this case meaning "term")... so it says "many terms Polynomials A polynomial looks like this: Term A number, a variable, or the

More information

Essential Question: What is a complex number, and how can you add, subtract, and multiply complex numbers? Explore Exploring Operations Involving

Essential Question: What is a complex number, and how can you add, subtract, and multiply complex numbers? Explore Exploring Operations Involving Locker LESSON 3. Complex Numbers Name Class Date 3. Complex Numbers Common Core Math Standards The student is expected to: N-CN. Use the relation i = 1 and the commutative, associative, and distributive

More information

Algebraic Expressions and Equations: Classification of Expressions and Equations *

Algebraic Expressions and Equations: Classification of Expressions and Equations * OpenStax-CNX module: m21848 1 Algebraic Expressions and Equations: Classification of Expressions and Equations * Wade Ellis Denny Burzynski This work is produced by OpenStax-CNX and licensed under the

More information

Sections 7.2, 7.3, 4.1

Sections 7.2, 7.3, 4.1 Sections 7., 7.3, 4.1 Section 7. Multiplying, Dividing and Simplifying Radicals This section will discuss the rules for multiplying, dividing and simplifying radicals. Product Rule for multiplying radicals

More information

17.1 Understanding Polynomial Expressions

17.1 Understanding Polynomial Expressions COMMON CORE 4 a b Locker x LESSON Common Core Math Standards The student is expected to: COMMON CORE A-SSE.A.a Interpret parts of an expression, such as terms, factors, and coefficients. Also A-SSE.A.b,

More information

2 P a g e. Essential Questions:

2 P a g e. Essential Questions: NC Math 1 Unit 5 Quadratic Functions Main Concepts Study Guide & Vocabulary Classifying, Adding, & Subtracting Polynomials Multiplying Polynomials Factoring Polynomials Review of Multiplying and Factoring

More information

Exponents ACTIVITY: Using Exponent Notation. ACTIVITY: Using Exponent Notation. How can you use exponents to. write numbers?

Exponents ACTIVITY: Using Exponent Notation. ACTIVITY: Using Exponent Notation. How can you use exponents to. write numbers? 6. Exponents write numbers? How can you use exponents to The expression 3 5 is called a power. The base is 3. The exponent is 5. base 3 5 exponent ACTIVITY: Using Exponent Notation Work with a partner.

More information

4.1 Understanding Polynomial Expressions

4.1 Understanding Polynomial Expressions 4 a b Locker x LESSON 4. Understanding Polynomial Expressions Common Core Math Standards The student is expected to: A-SSE.a Interpret parts of an expression, such as terms, factors, and coefficients.

More information

Section 5.1 Practice Exercises. Vocabulary and Key Concepts

Section 5.1 Practice Exercises. Vocabulary and Key Concepts Section 5.1 Practice Exercises Vocabulary and Key Concepts 1. 1. A(n) is used to show repeated multiplication of the base. 2. For b 0, the expression b 0 is defined to be. 3. For b 0, the expression b

More information

Maintaining Mathematical Proficiency

Maintaining Mathematical Proficiency Chapter Maintaining Mathematical Proficiency Simplify the expression. 1. 8x 9x 2. 25r 5 7r r + 3. 3 ( 3x 5) + + x. 3y ( 2y 5) + 11 5. 3( h 7) 7( 10 h) 2 2 +. 5 8x + 5x + 8x Find the volume or surface area

More information

Unit 3 Vocabulary. An algebraic expression that can contains. variables, numbers and operators (like +, An equation is a math sentence stating

Unit 3 Vocabulary. An algebraic expression that can contains. variables, numbers and operators (like +, An equation is a math sentence stating Hart Interactive Math Algebra 1 MODULE 2 An algebraic expression that can contains 1 Algebraic Expression variables, numbers and operators (like +,, x and ). 1 Equation An equation is a math sentence stating

More information

6.2 Multiplying Polynomials

6.2 Multiplying Polynomials Locker LESSON 6. Multiplying Polynomials PAGE 7 BEGINS HERE Name Class Date 6. Multiplying Polynomials Essential Question: How do you multiply polynomials, and what type of epression is the result? Common

More information

CP Algebra 2. Unit 2-1 Factoring and Solving Quadratics

CP Algebra 2. Unit 2-1 Factoring and Solving Quadratics CP Algebra Unit -1 Factoring and Solving Quadratics Name: Period: 1 Unit -1 Factoring and Solving Quadratics Learning Targets: 1. I can factor using GCF.. I can factor by grouping. Factoring Quadratic

More information

Algebra. Practice Pack

Algebra. Practice Pack Algebra Practice Pack WALCH PUBLISHING Table of Contents Unit 1: Algebra Basics Practice 1 What Are Negative and Positive Numbers?... 1 Practice 2 Larger and Smaller Numbers................ 2 Practice

More information

5.1 Modelling Polynomials

5.1 Modelling Polynomials 5.1 Modelling Polynomials FOCUS Model, write, and classify polynomials. In arithmetic, we use Base Ten Blocks to model whole numbers. How would you model the number 234? In algebra, we use algebra tiles

More information

Algebra Summer Review Packet

Algebra Summer Review Packet Name: Algebra Summer Review Packet About Algebra 1: Algebra 1 teaches students to think, reason, and communicate mathematically. Students use variables to determine solutions to real world problems. Skills

More information

Algebra I. Exponents and Polynomials. Name

Algebra I. Exponents and Polynomials. Name Algebra I Exponents and Polynomials Name 1 2 UNIT SELF-TEST QUESTIONS The Unit Organizer #6 2 LAST UNIT /Experience NAME 4 BIGGER PICTURE DATE Operations with Numbers and Variables 1 CURRENT CURRENT UNIT

More information

How can you find decimal approximations of square roots that are not rational? ACTIVITY: Approximating Square Roots

How can you find decimal approximations of square roots that are not rational? ACTIVITY: Approximating Square Roots . Approximating Square Roots How can you find decimal approximations of square roots that are not rational? ACTIVITY: Approximating Square Roots Work with a partner. Archimedes was a Greek mathematician,

More information

Solving Polynomial Equations 3.5. Essential Question How can you determine whether a polynomial equation has a repeated solution?

Solving Polynomial Equations 3.5. Essential Question How can you determine whether a polynomial equation has a repeated solution? 3. Solving Polynomial Equations Essential Question Essential Question How can you determine whether a polynomial equation has a repeated solution? Cubic Equations and Repeated Solutions USING TOOLS STRATEGICALLY

More information

Polynomials. This booklet belongs to: Period

Polynomials. This booklet belongs to: Period HW Mark: 10 9 8 7 6 RE-Submit Polynomials This booklet belongs to: Period LESSON # DATE QUESTIONS FROM NOTES Questions that I find difficult Pg. Pg. Pg. Pg. Pg. Pg. Pg. Pg. Pg. Pg. REVIEW TEST Your teacher

More information

Math 10 - Unit 5 Final Review - Polynomials

Math 10 - Unit 5 Final Review - Polynomials Class: Date: Math 10 - Unit 5 Final Review - Polynomials Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Factor the binomial 44a + 99a 2. a. a(44 + 99a)

More information

LESSON 9.1 ROOTS AND RADICALS

LESSON 9.1 ROOTS AND RADICALS LESSON 9.1 ROOTS AND RADICALS LESSON 9.1 ROOTS AND RADICALS 67 OVERVIEW Here s what you ll learn in this lesson: Square Roots and Cube Roots a. Definition of square root and cube root b. Radicand, radical

More information

Complex Numbers. Essential Question What are the subsets of the set of complex numbers? Integers. Whole Numbers. Natural Numbers

Complex Numbers. Essential Question What are the subsets of the set of complex numbers? Integers. Whole Numbers. Natural Numbers 3.4 Complex Numbers Essential Question What are the subsets of the set of complex numbers? In your study of mathematics, you have probably worked with only real numbers, which can be represented graphically

More information

ACTIVITY: Estimating the Area of a Circle

ACTIVITY: Estimating the Area of a Circle 8. Areas of Circles How can you find the area of a circle? ACTIVITY: Estimating the Area of a Circle Work with a partner. Each square in the grid is unit by unit. a. Find the area of the large 0-by-0 square.

More information

7.2 Multiplying Polynomials

7.2 Multiplying Polynomials Locker LESSON 7. Multiplying Polynomials Teas Math Standards The student is epected to: A.7.B Add, subtract, and multiply polynomials. Mathematical Processes A.1.E Create and use representations to organize,

More information

Shenandoah University. (PowerPoint) LESSON PLAN *

Shenandoah University. (PowerPoint) LESSON PLAN * Shenandoah University (PowerPoint) LESSON PLAN * NAME DATE 10/28/04 TIME REQUIRED 90 minutes SUBJECT Algebra I GRADE 6-9 OBJECTIVES AND PURPOSE (for each objective, show connection to SOL for your subject

More information

Simplifying Rational Expressions

Simplifying Rational Expressions .3 Simplifying Rational Epressions What are the ecluded values of a rational epression? How can you simplify a rational epression? ACTIVITY: Simplifying a Rational Epression Work with a partner. Sample:

More information

Why is the product of two negative rational numbers positive?

Why is the product of two negative rational numbers positive? . Multiplying and Dividing Rational Numbers Why is the product of two negative rational numbers positive? In Section., you used a table to see that the product of two negative integers is a positive integer.

More information

Answer Key. Solve each equation x - 9 = (n + 2) = b - 6 = -3b + 48

Answer Key. Solve each equation x - 9 = (n + 2) = b - 6 = -3b + 48 Solve each equation. 1. -3x - 9 = -27 2. 25 + 2(n + 2) = 30 3. -9b - 6 = -3b + 48 x = 6 n = 1 / 2 b = -9 4. 5 - (m - 4) = 2m + 3(m - 1) 5. -24-10k = -8(k + 4) - 2k 6. f - (-19) = 11f + 23-20f m = 2 no

More information

LESSON 6.2 POLYNOMIAL OPERATIONS I

LESSON 6.2 POLYNOMIAL OPERATIONS I LESSON 6. POLYNOMIAL OPERATIONS I LESSON 6. POLYNOMIALS OPERATIONS I 63 OVERVIEW Here's what you'll learn in this lesson: Adding and Subtracting a. Definition of polynomial, term, and coefficient b. Evaluating

More information

5-1 Study Guide and Intervention

5-1 Study Guide and Intervention 5-1 Study Guide and Intervention Multiply and Divide Monomials Negative exponents are a way of expressing the multiplicative inverse of a number. Negative Exponents a -n = 1 a n and 1 a -n = a n for any

More information

Algebra II Chapter 5: Polynomials and Polynomial Functions Part 1

Algebra II Chapter 5: Polynomials and Polynomial Functions Part 1 Algebra II Chapter 5: Polynomials and Polynomial Functions Part 1 Chapter 5 Lesson 1 Use Properties of Exponents Vocabulary Learn these! Love these! Know these! 1 Example 1: Evaluate Numerical Expressions

More information

Lesson 3 Algebraic expression: - the result obtained by applying operations (+, -,, ) to a collection of numbers and/or variables o

Lesson 3 Algebraic expression: - the result obtained by applying operations (+, -,, ) to a collection of numbers and/or variables o Lesson 3 Algebraic expression: - the result obtained by applying operations (+, -,, ) to a collection of numbers and/or variables o o ( 1)(9) 3 ( 1) 3 9 1 Evaluate the second expression at the left, if

More information

7-7 Multiplying Polynomials

7-7 Multiplying Polynomials Example 1: Multiplying Monomials A. (6y 3 )(3y 5 ) (6y 3 )(3y 5 ) (6 3)(y 3 y 5 ) 18y 8 Group factors with like bases together. B. (3mn 2 ) (9m 2 n) Example 1C: Multiplying Monomials Group factors with

More information

Think of three math problems using the four operations where order matters and three where order doesn t matter. ACTIVITY: Commutative Properties

Think of three math problems using the four operations where order matters and three where order doesn t matter. ACTIVITY: Commutative Properties 3.3 Properties of Addition and Multiplication operation matter? Does the order in which you perform an ACTIVITY: Does Order Matter? Work with a partner. Place each statement in the correct oval. a. Fasten

More information

8-1 Factors and Greatest Common Factors 8-1. Factors and Greatest Common Factors

8-1 Factors and Greatest Common Factors 8-1. Factors and Greatest Common Factors 8-1 Factors and Greatest Common Factors Warm Up Lesson Presentation Lesson Quiz 1 2 pts 2 pts Bell Quiz 8-1 Tell whether the second number is a factor of the first number 1. 50, 6 2 pts no 2. 105, 7 3.

More information

LESSON 7.2 FACTORING POLYNOMIALS II

LESSON 7.2 FACTORING POLYNOMIALS II LESSON 7.2 FACTORING POLYNOMIALS II LESSON 7.2 FACTORING POLYNOMIALS II 305 OVERVIEW Here s what you ll learn in this lesson: Trinomials I a. Factoring trinomials of the form x 2 + bx + c; x 2 + bxy +

More information

6-3 Polynomials. Warm Up Lesson Presentation Lesson Quiz. Holt McDougal Algebra 1

6-3 Polynomials. Warm Up Lesson Presentation Lesson Quiz. Holt McDougal Algebra 1 6-3 Polynomials Warm Up Lesson Presentation Lesson Quiz Algebra 1 Objectives Classify polynomials and write polynomials in standard form. Evaluate polynomial expressions. A polynomial is a monomial or

More information

1.1 Modeling with Area

1.1 Modeling with Area 1.1 Modeling with Area Essential Question How can you use the population and area of a region to describe how densely the region is populated? Exploring Population and Area Work with a partner. Use the

More information

UNIT 9 (Chapter 7 BI) Polynomials and Factoring Name:

UNIT 9 (Chapter 7 BI) Polynomials and Factoring Name: UNIT 9 (Chapter 7 BI) Polynomials and Factoring Name: The calendar and all assignments are subject to change. Students will be notified of any changes during class, so it is their responsibility to pay

More information

9-1 Skills Practice Factors and Greatest Common Factors Find the factors of each number. Then classify each number as prime or composite

9-1 Skills Practice Factors and Greatest Common Factors Find the factors of each number. Then classify each number as prime or composite 9-1 Skills Practice Factors and Greatest Common Factors Find the factors of each number. Then classify each number as prime or composite. 1. 10 2. 31 3. 16 4. 52 5. 38 6. 105 Find the prime factorization

More information

Common Core Algebra 2 Review Session 1

Common Core Algebra 2 Review Session 1 Common Core Algebra 2 Review Session 1 NAME Date 1. Which of the following is algebraically equivalent to the sum of 4x 2 8x + 7 and 3x 2 2x 5? (1) 7x 2 10x + 2 (2) 7x 2 6x 12 (3) 7x 4 10x 2 + 2 (4) 12x

More information